Question

已知x+y分之xy=-2,y+z分之yz=3分之4,z+x分之zx=-3分之4,问xy+yz+zx分之xyz的值?

Answer 1

x+y分之xy=-2

∴(x+y)/xy=-1/2

1/x+1/y=-1/2 (4)

,y+z分之yz=3分之4

1/y+1/z=3/4 (5)

,z+x分之zx=-3分之4

1/x+1/z=-3/4 (6)

(4)+(5)+(6)得

2/x+2/y+2/z=1/2

1/x+1/y+1/z=1/4

∴(xy+yz+xz)/xyz=1/4

xyz/(xy+yz+xz)=4